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C₈×D₂₁ #66621

order	336
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₈×D₂₁

Splittings

Fitting	C₃×C₇×C₈ ⋊ C₂
derived, Hall	C₃×C₇ ⋊ C₂×C₈
Sylow	C₇ ⋊ D₃×C₈
Sylow	C₃ ⋊ C₈×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₈	D₂₁
commutator, hypocenter	C₃×C₇	C₂×C₈
Frattini	C₄	C₂×D₂₁
Fitting	C₃×C₇×C₈	C₂
socle	C₂×C₃×C₇	C₂×C₄
prime radical	C₂×D₂₁	C₄
cosocle	C₃×C₄×C₇	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₈

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₂₁⋊C₁₆, #10620471, C₁₆×D₂₁, …
maximal normal subgroup of	D₂₁⋊C₁₆, #10620471, C₁₆×D₂₁, …
maximal quotient of	C₁₆×D₂₁, #10620637, C₈×Dic₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 90);