Finite Group Databasebeta

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C4⋊C4×C11⋊C16 #14669117

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×C11⋊C16

Splittings

SylowC11 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D11
commutatorC2×C11C2×C4×C16
FittingC8×C11×C4⋊C4C2
socle, prime radicalC23×C11C22×C8
cosocleC22×C8×C11C23
hypercenterC8×C4⋊C4D11
hypocenterC11C16×C4⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84912);