Finite Group Databasebeta

C2×#28385428 #43273084

order28736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28385428

Splittings

SylowC449 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#14267798
commutatorC2×C449C23×C4
FrattiniC2C23×#14267798
FittingC2×Q8×C449C4
socleC22×C449C22×C4
prime radicalC2×#20297737C2
cosocleDic449C24
hypercenterC2×Q8#14267798
hypocenterC449C2×#131
LCSG ▷ C2×C449 ▷ C449
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14368

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28736, 1626);