Finite Group Databasebeta

C23×#14519758 #30586659

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×#14519758

Splittings

SylowC61 ⋊ C23×#123

Subgroups

subgroupG/H
centerC25C22×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
Fitting, prime radicalC24×D4×C61C2
socleC25×C61C23
hypercenterC24×D4D61
hypocenterC61C23×#123
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C25 ◁ C24×D4

15150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

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, 1076214);