Finite Group Databasebeta

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C2×C4⋊C4×Dic22 #14913075

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4⋊C4×Dic22

Splittings

SylowC11 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×Q8×C4⋊C4
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328870);