Finite Group Databasebeta

C4×C22⋊C8×D61 #29677522

order15616
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×C22⋊C8×D61

Splittings

FittingC4×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D61
commutatorC2×C61C22×C4×C8
FrattiniC22×C4C23×D61
FittingC4×C22⋊C8×C61C2
socleC23×C61C23×C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenterC4×C22⋊C8D61
hypocenterC61C2×C4×C22⋊C8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167077);