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H(5,𝔽2)×C467 #28417856

order14944
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C467 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C467

Subgroups

subgroupG/H
center, socleC2×C467C24
commutator, Frattini, cosocleC2C24×C467
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C467 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3736

Conjugacy classes & character table

7939 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44470205, #44470215, #44470224, …
maximal subgroup of#453×C467, #455×C467, B(4,𝔽2)×C467, …
maximal normal subgroup of#453×C467, #455×C467, B(4,𝔽2)×C467, …
maximal quotient of#518×C467, #520×C467, #534×C467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14944, 49);