Finite Group Databasebeta

C2×#21418526 #28416956

order14912
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21418526

Splittings

SylowC233 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D233
commutator, cosocleC22×C233C24
FrattiniC22C23×D233
FittingC2×C4⋊C4×C233C2
socle, prime radicalC23×C233C23
hypercenterC2×C4⋊C4D233
hypocenterC233C2×#125
LCSG ▷ C22×C233 ▷ C233
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14912

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1070);