Finite Group Databasebeta

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C2×C8×C4⋊Dic61 #29677941

order15616
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C8×C4⋊Dic61

Splittings

SylowC61 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC23×C8C2×D61
commutatorC2×C61C22×C4×C8
FrattiniC22×C4C23×D61
FittingC22×C4×C8×C61C2
socle, prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenterC22×C4×C8D61
hypocenterC61C2×C8×C4⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167496);