Finite Group Databasebeta

C23×#10596957 #18011581

order4736
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#10596957

Splittings

SylowC37 ⋊ C23×M16

Subgroups

subgroupG/H
centerC24C2×#3866
commutatorC2×C37C24×C4
FrattiniC2C24×#3866
Fitting, prime radicalC25×C37C4
socleC24×C37C2×C4
cosocleDic37C25
hypercenterC25#3866
hypocenterC37C23×M16
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C24 ◁ C25

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21495);