Finite Group Databasebeta

C2×#13133807 #16812124

order3424
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13133807

Splittings

FittingC2×C8×C107 ⋊ C2
SylowC107 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22D428
commutator, cosocleC4×C107C23
FrattiniC4C22×D107
FittingC2×C8×C107C2
socleC22×C107D4
prime radicalC2×D428C2
hypercenterC2×C8D107
hypocenterC107C2×SD16
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3424, 161);