Finite Group Databasebeta

C2×#88240 #11719624

order832
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#88240

Splittings

SylowC13 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#261
commutatorC2×C13C23×C4
FrattiniC2C23×#261
FittingC2×Q8×C13C4
socleC22×C13C22×C4
prime radicalC2×#6131C2
cosocleDic13C24
hypercenterC2×Q8#261
hypocenterC13C2×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13130595, #13130613, #13130617, …
maximal normal subgroup of#13130595, #13130613, #13130617, …
maximal quotient ofC2×#11719072, C4×#88240, C2×#11719159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1590);