Finite Group Databasebeta

C2×#24905554 #35319280

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24905554

Splittings

SylowC83 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC24#13050575
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC22×#107×C83C2
socle, prime radicalC24×C83D8
cosocleC22×C8×C83C23
hypercenterC22×#107D83
hypocenterC83C2×#1380
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84444);