Finite Group Databasebeta

C23×#14519753 #30586653

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

Aliases

direct productC23×#14519753

Splittings

FittingC24×Q8×C61 ⋊ C2
SylowC61 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC25C22×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC24×Q8×C61C2
socleC25×C61C23
prime radicalC25×D61C22
hypercenterC24×Q8D61
hypocenterC61C23×C22⋊Q8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C25 ◁ C24×Q8

14078 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, 1076208);