Finite Group Databasebeta

C2×#13133151 #16810657

order3392
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13133151

Splittings

SylowC53 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D212
commutatorC4×C53C22×C4
FrattiniC2×C4C22×D53
FittingC22×C8×C53C2
socle, prime radicalC23×C53D4
cosocleC2×C4×C53C23
hypercenterC22×C8D53
hypocenterC53C2×#107
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3392, 583);