Finite Group Databasebeta

C2×#14558560 #18011298

order4736
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14558560

Splittings

SylowC37 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC23C22×#3866
commutatorC2×C37C23×C8
FrattiniC22C23×#3866
FittingC2×C22⋊C4×C37C4
socleC23×C37C22×C4
prime radicalC22×C22⋊D37C4
cosocleC2×Dic37C24
hypercenterC2×C22⋊C4#3866
hypocenterC37C2×C8×D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C22⋊C4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21212);