Finite Group Databasebeta

C2×#17984778 #22580999

order8896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#17984778

Splittings

SylowC139 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D556
commutatorC4×C139C22×C4
FrattiniC2×C4C22×D139
FittingC22×C8×C139C2
socleC22×C139C4⋊C4
hypercenterC22×C8D139
hypocenterC139C2×#108
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2236 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#31804497, #31804498, #31804499, …
maximal normal subgroup of#31804497, #31804498, #31804499, …
maximal quotient ofC2×#22580704, C2×#22580706, #31805152, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 595);