Finite Group Databasebeta

C2×#13095498 #15690823

order3104
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13095498

Splittings

FittingC2×Q8×C97 ⋊ C2
SylowC97 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D97
commutator, cosocleC4×C97C23
FrattiniC4C22×D97
FittingC2×Q8×C97C2
socleC22×C97D4
prime radicalC2×D388C2
hypercenterC2×Q8D97
hypocenterC97C2×SD16
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1552

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 159);