Finite Group Databasebeta

← Prev (#88984) Next (#88986) →

C₂×C₃×#622 #88985

order	432
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃×#622

Splittings

derived	C₃² ⋊ C₂×C₃×C₈
Sylow	C₃³ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	#157
commutator, hypocenter	C₃²	C₂×C₃×C₈
Frattini	C₂	C₂×C₃×#157
Fitting, socle, prime radical	C₂²×C₃³	C₄
cosocle	C₃⋊Dic₃	C₂²×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₃

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

(3,4,5)(6,7)(8,9,10,11)(12,13,14,16,15,17,18,19);(1,2)(6,10,8)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃×#622, #11722724, (C₂×D₃)⋊#622, …
maximal normal subgroup of	Dic₃×#622, #11722724, (C₂×D₃)⋊#622, …
maximal quotient of	C₂×C₃×#3708, C₃×#63773, C₃×C₄×#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 632);