Finite Group Databasebeta

C2×#14273663 #16837448

order3776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14273663

Splittings

SylowC59 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D236
commutatorC4×C59C22×C4
FrattiniC2×C4C22×D59
FittingC22×C8×C59C2
socleC22×C59C4⋊C4
prime radicalC23×C59Q8
cosocleC2×C4×C59C23
hypercenterC22×C8D59
hypocenterC59C2×#108
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 595);