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C2×C8×Dic254 #30647651

order16256
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×Dic254

Splittings

SylowC127 ⋊ C2×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C2×D127
commutatorC2×C127C23×C8
FrattiniC2×C4C23×D127
FittingC2×C4×C8×C127C2
socle, prime radicalC23×C127C22×C4
cosocleC2×C4×C127C24
hypercenterC2×C4×C8D127
hypocenterC127C2×C8×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

440 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13431);