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H(5,𝔽2)×C421 #27212269

order13472
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C421 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C421

Subgroups

subgroupG/H
center, socleC2×C421C24
commutator, Frattini, cosocleC2C24×C421
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C421 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3368

Conjugacy classes & character table

7157 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41003008, #41003018, #41003027, …
maximal subgroup of#453×C421, #455×C421, B(4,𝔽2)×C421, …
maximal normal subgroup of#453×C421, #455×C421, B(4,𝔽2)×C421, …
maximal quotient of#518×C421, #520×C421, #534×C421, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13472, 49);