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C2×C4⋊C4×C22⋊D11 #14913057

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4⋊C4×C22⋊D11

Splittings

FittingC23×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC23×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC23×C4⋊C4D11
hypocenterC11C2×D4×C4⋊C4
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 328852);