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C2×H(5,𝔽2)×C233 #28416150

order14912
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C233 · Schur multiplier (H2) = C29

Aliases

direct productC2×H(5,𝔽2)×C233

Subgroups

subgroupG/H
center, socleC22×C233C24
commutator, Frattini, cosocleC2C25×C233
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C233 ◁ G

898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3728

Conjugacy classes & character table

7922 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#1790×C233, #1792×C233, #1795×C233, …
maximal normal subgroup of#1790×C233, #1792×C233, #1795×C233, …
maximal quotient ofC2×#518×C233, C2×#520×C233, C4×H(5,𝔽2)×C233, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 264);