D₄₇×#3557 #27123720

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

D₄₇×#3557

Splittings

Fitting	C₄₇×#3557 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3557

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3557	C₂
prime radical	#540×D₄₇	C₂
hypercenter	#3557	D₄₇
hypocenter	C₄₇	C₂×#3557
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3557

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 6 generators on 79 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(64,68,69,67)(65,73,71,72)(66,76,75,77)(70,78,74,79);(49,55)(53,62)(54,58)(61,63)(64,67,69,68)(65,72,71,73)(66,76,75,77)(70,78,74,79);(48,51,52,60)(49,54,55,58)(50,56,57,59)(53,61,62,63)(65,71)(66,75)(72,73)(76,77);(48,50,52,57)(49,53,55,62)(51,59,60,56)(54,63,58,61)(64,66,69,75)(65,70,71,74)(67,77,68,76)(72,79,73,78);(48,49)(50,53)(51,58)(52,55)(54,60)(56,63)(57,62)(59,61)(64,65)(66,74)(67,73)(68,72)(69,71)(70,75)(76,78)(77,79);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)

Conjugacy classes & character table

950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1077010);

D47×#3557 #27123720