Finite Group Databasebeta

C2×#24905713 #35326074

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24905713

Splittings

SylowC83 ⋊ C2×#1441

Subgroups

subgroupG/H
centerC25C22×D83
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC23×C4⋊C4×C83C2
socle, prime radicalC25×C83C23
cosocleC24×C83C24
hypercenterC23×C4⋊C4D83
hypocenterC83C2×#1441
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C25 ◁ C23×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 91238);