Finite Group Databasebeta

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C4×Dic1016 #30640590

order16256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1016

Splittings

SylowC127 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D1016
commutatorC8×C127C22×C4
FrattiniC2×C8C22×D127
FittingC4×C16×C127C2
socle, prime radicalC22×C127C2×D8
cosocleC2×C8×C127C23
hypercenterC4×C16D127
hypocenterC127C4×Q32
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6370);