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C2×C4×C8×D127 #30647129

order16256
isoclinismisoclinic class of D127
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D127

Splittings

FittingC2×C4×C8×C127 ⋊ C2
derived, SylowC127 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D127
commutator, hypocenterC127C22×C4×C8
FrattiniC2×C4C23×D127
FittingC2×C4×C8×C127C2
socleC23×C127C22×C4
prime radicalC23×D127C2×C4
cosocleC2×C4×C127C24
LCSG ▷ C127
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 12909);