Finite Group Databasebeta

C2×C8×C4⋊#6923 #30614210

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

Aliases

direct productC2×C8×C4⋊#6923

Splittings

FittingC2×C4×C8×C61 ⋊ C4
SylowC61 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C2×#6923
commutatorC2×C61C22×C4×C8
FrattiniC2×C4C23×#6923
FittingC2×C4×C8×C61C4
socleC23×C61C2×C42
prime radicalC23×D61C22×C4
cosocleC2×C4×D61C24
hypercenterC2×C4×C8#6923
hypocenterC61C2×C8×C4⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103765);