D₄₇×#2875 #27079684

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

D₄₇×#2875

Splittings

Fitting	C₄₇×#2875 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2875

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Fitting	C₄₇×#2875	C₂
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₂×#41×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2875	D₄₇
hypocenter	C₄₇	C₂×#2875
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2875

3278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 67 points:

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

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1032974);

D47×#2875 #27079684