Finite Group Databasebeta

C2×#20297311 #28384343

order14272
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20297311

Splittings

SylowC223 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D223
commutatorC2×C223C23×C4
FrattiniC4C23×D223
Fitting, prime radicalC2×#41×C223C2
socleC22×C223C22×C4
cosocleC4×C223C24
hypercenterC2×#41D223
hypocenterC223C2×#131
LCSG ▷ C2×C223 ▷ C223
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7136

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14272, 1312);