Finite Group Databasebeta

C2×#24905511 #35315643

order21248
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#24905511

Splittings

SylowC83 ⋊ C2×#1362

Subgroups

subgroupG/H
centerC23#14581712
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC2×#335×C83C2
socle, prime radicalC23×C83#102
cosocleC4×C8×C83C23
hypercenterC2×#335D83
hypocenterC83C2×#1362
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#335

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 80807);