Finite Group Databasebeta

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C2×C4×C4⋊Dic127 #30641065

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic127

Splittings

SylowC127 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D127
commutatorC2×C127C22×C42
FrattiniC23C23×D127
FittingC22×C42×C127C2
socle, prime radicalC24×C127C23
cosocleC23×C127C24
hypercenterC22×C42D127
hypocenterC127C2×C4×C4⋊C4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C23×C4 ◁ C22×C42

928 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, 6845);