Finite Group Databasebeta

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C4×#10622607 #14675629

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#10622607

Splittings

FittingC2×C4×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C4×#396

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4×#396
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 91424);