Finite Group Databasebeta

C23×C22⋊#92418 #30543440

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊#92418

Splittings

SylowC61 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D61
commutatorC2×C61C24×C8
FrattiniC2×C4C24×D61
FittingC25×C4×C61C2
socleC25×C61C2×C4
prime radicalC26×C61C4
cosocleC2×C4×C61C25
hypercenterC25×C4D61
hypocenterC61C23×C22⋊C8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1032995);