Finite Group Databasebeta

C2×C4×#88102 #16797190

order3328
isoclinismisoclinic class of #88101
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#88102

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C2×C4×#107

Subgroups

subgroupG/H
centerC22×C4C4⋊#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C4⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C2×C4×#107
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103839);