Finite Group Databasebeta

D8×C22⋊Dic61 #29695837

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×C22⋊Dic61

Splittings

SylowC61 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC23×D8×C61C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC23×D8D61
hypocenterC61C22⋊C4×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 185392);