Finite Group Databasebeta

C4×#11745672 #16837495

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

Aliases

direct productC4×#11745672

Splittings

SylowC59 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4C22⋊D59
commutatorC4×C59C22×C4
FrattiniC2×C4C22×D59
FittingC4×Q8×C59C2
socle, prime radicalC22×C59C2×D4
cosocleC2×C4×C59C23
hypercenterC4×Q8D59
hypocenterC59C4×Q16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 642);