Finite Group Databasebeta

C22×#22604426 #49149020

order36928
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#22604426

Splittings

derived, SylowC577 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#14556313
commutator, hypocenterC577C23×C8
FrattiniC2C23×#14556313
FittingC22×C4×C577C4
socleC23×C577C2×C4
prime radicalC23×D577C4
cosocleDic577C24
LCSG ▷ C577
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

2368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1620);