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C₃×Dic₂₈ #66593

order	336
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₂₈

Splittings

Hall	C₃×C₇ ⋊ Q₁₆
Sylow	C₇ ⋊ C₃×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	D₂₈
commutator, cosocle	C₄×C₇	C₂²×C₃
Frattini	C₄	C₂×C₃×D₇
Fitting	C₃×C₇×C₈	C₂
socle, prime radical	C₂×C₃×C₇	D₄
hypercenter	C₃×C₈	D₇
hypocenter	C₇	C₃×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3)(4,5,6,7,8,9,10,11)(12,19,18,17,16,15,14,13)(20,21,22,23,24,25,26);(4,12,8,16)(5,13,9,17)(6,14,10,18)(7,15,11,19)(21,26)(22,25)(23,24)

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10620476, #10620478, #10620481, …
maximal normal subgroup of	#10620476, #10620478, #10620481, …
maximal quotient of	C₃×#6390, C₃×#6392, C₂×C₃×Dic₂₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 62);