Finite Group Databasebeta

C2×#88058 #11718766

order832
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#88058

Splittings

SylowC13 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D52
commutatorC4×C13C22×C4
FrattiniC2×C4C22×D13
FittingC22×C8×C13C2
socle, prime radicalC23×C13D4
cosocleC2×C4×C13C23
hypercenterC22×C8D13
hypocenterC13C2×#107
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13112927, #13112928, #13112945, …
maximal normal subgroup of#13112927, #13112928, #13112945, …
maximal quotient ofC2×#11718050, #13113595, #13113611, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 732);