Finite Group Databasebeta

C2×#20301058 #28412493

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20301058

Splittings

SylowC229 ⋊ C2×#108

Subgroups

subgroupG/H
centerC22C4⋊#11745021
commutatorC4×C229C22×C4
FrattiniC4C22×#11745021
FittingC2×C8×C229C4
socleC22×C229C4⋊C4
prime radicalC22×D229Q8
cosocleC4×D229C23
hypercenterC2×C8#11745021
hypocenterC229C2×#108
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1561);