Finite Group Databasebeta

C22×#11924611 #18011559

order4736
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11924611

Splittings

SylowC37 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C4C2×#3866
commutatorC2×C37C23×C8
FrattiniC4C23×#3866
FittingC22×C8×C37C4
socleC23×C37C2×C8
prime radicalC23×D37C8
cosocle#64436C24
hypercenterC22×C8#3866
hypocenterC37C22×M32
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C22×C8

400 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, 21473);