Finite Group Databasebeta

C23×#14519747 #30586645

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C216

Aliases

direct productC23×#14519747

Splittings

FittingC23×C22⋊C4×C61 ⋊ C2
SylowC61 ⋊ C23×#120

Subgroups

subgroupG/H
centerC25C22×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC23×C22⋊C4×C61C2
socleC25×C61C23
hypercenterC23×C22⋊C4D61
hypocenterC61C23×#120
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C25 ◁ C23×C22⋊C4

42862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076200);