Finite Group Databasebeta

C2×#13129893 #16789095

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13129893

Splittings

FittingC2×C13×#107 ⋊ C4
SylowC13 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC23#88115
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC23×C13#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC2×#107#261
hypocenterC13C2×#1380
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095744);