Finite Group Databasebeta

C2×#20301076 #28412558

order14656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20301076

Splittings

SylowC229 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#11745021
commutatorC2×C229C23×C4
FrattiniC2C23×#11745021
FittingC2×Q8×C229C4
socleC22×C229C22×C4
prime radicalC2×#16814667C2
cosocleDic229C24
hypercenterC2×Q8#11745021
hypocenterC229C2×#131
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1626);