#88363

order	432
isoclinism	isoclinic class of Dic₅₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Sylow

C₂₇ ⋊ M₁₆

Subgroups

	subgroup	G/H
center	C₄	C₂×D₂₇
commutator	C₂×C₂₇	C₂×C₄
Frattini	C₄×C₉	C₂×D₃
Fitting	C₂×C₄×C₂₇	C₂
socle	C₂×C₃	C₂×Dic₉
prime radical	C₂²×C₃	Dic₉
cosocle	C₄×C₂₇	C₂²
hypercenter	C₂×C₄	D₂₇
hypocenter	C₂₇	M₁₆
LCS	G ▷ C₂×C₂₇ ▷ C₂₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 2 generators on 35 points:

(1,25,24,10,8,5,22,20,23,4,7,26,9,19,14,3,27,6,12,17,13,21,2,18,11,16,15)(29,32)(33,35);(2,5)(3,9)(4,12)(6,7)(8,18)(10,11)(13,20)(14,19)(15,25)(16,24)(17,23)(21,22)(26,27)(28,29,30,33,31,32,34,35)

Polycyclic presentation:

2^4,3^3|a^2=c,c^2=d,e^3=f^2g,f^3=g^2,b^a=bd,e^a=e^2f,f^a=f^2g,g^a=g^2

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11720045, #11720053, #11720062, …
maximal normal subgroup of	#11720045, #11720053, #11720062, …
maximal quotient of	#11720043, C₄⋊(C₂₇⋊C₈), #11720070, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 10);