Finite Group Databasebeta

C2×#14273647 #16837388

order3776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14273647

Splittings

FittingC2×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D59
commutatorC4×C59C22×C4
FrattiniC2×C4C22×D59
FittingC2×C4⋊C4×C59C2
socleC23×C59D4
prime radicalC22×D236C2
cosocleC2×C4×C59C23
hypercenterC2×C4⋊C4D59
hypocenterC59C2×#102
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 535);