Finite Group Databasebeta

C2×#13083558 #15668017

order2848
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13083558

Splittings

SylowC89 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D89
commutatorC2×C89C22×C4
FrattiniC4C22×D89
FittingC22×C4×C89C2
socleC22×C89C2×C4
prime radicalC23×C89C4
cosocleC4×C89C23
hypercenterC22×C4D89
hypocenterC89C2×M16
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1424

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2848, 151);