Finite Group Databasebeta

C4×#11924542 #18003016

order4736
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11924542

Splittings

FittingC2×C4×C8×C37 ⋊ C2
SylowC37 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D37
commutatorC2×C37C22×C42
FrattiniC2×C4C23×D37
FittingC2×C4×C8×C37C2
socleC22×C37C23×C4
prime radicalC2×#10596962C22
cosocleC2×C4×C37C24
hypercenterC2×C4×C8D37
hypocenterC37C4×#131
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 12930);