Finite Group Databasebeta

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C4×#10623369 #15618016

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

Aliases

direct productC4×#10623369

Splittings

FittingC4×C11×2−1+4 ⋊ C2
SylowC11 ⋊ C4×#578

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC4×C11×2−1+4C2
socleC22×C11C23×D4
prime radicalC2×#10623369C2
cosocleC2×C4×C11C25
hypercenterC4×2−1+4D11
hypocenterC11C4×#578
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

2658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033811);