Finite Group Databasebeta

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C2×C4×Q8×D127 #30651903

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×Q8×D127

Splittings

FittingC2×C4×Q8×C127 ⋊ C2
SylowC127 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC2×C127C24×C4
FrattiniC22C24×D127
FittingC2×C4×Q8×C127C2
socleC23×C127C24
prime radicalC23×D127C23
cosocleC22×C127C25
hypercenterC2×C4×Q8D127
hypocenterC127C22×C4×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17683);