Finite Group Databasebeta

C2×#14273670 #16837825

order3776
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14273670

Splittings

FittingC2×Q16×C59 ⋊ C2
SylowC59 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#11745669
commutator, cosocleC8×C59C23
FrattiniC8C22×D59
FittingC2×Q16×C59C2
socleC22×C59D8
prime radicalC2×D472C2
hypercenterC2×Q16D59
hypocenterC59C2×SD32
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 972);