C₂²×#16837310 #28754864

order	15104
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

direct product

C₂²×#16837310

Splittings

Fitting	C₂⁴×D₄×C₅₉ ⋊ C₂
Sylow	C₅₉ ⋊ C₂²×#392

Subgroups

	subgroup	G/H
center	C₂⁵	C₂²×D₅₉
commutator, cosocle	C₂³×C₅₉	C₂⁵
Frattini	C₂³	C₂⁴×D₅₉
Fitting	C₂⁴×D₄×C₅₉	C₂
socle	C₂⁵×C₅₉	C₂³
hypercenter	C₂⁴×D₄	D₅₉
hypocenter	C₅₉	C₂²×#392
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×D₄

13646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 5 generators on 75 points:

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

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 335743);

C22×#16837310 #28754864