Finite Group Databasebeta

C2×#24905581 #35319343

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

Aliases

direct productC2×#24905581

Splittings

SylowC83 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC23#14581707
commutatorC23×C83C2×C42
FrattiniC22×D4C22×D83
FittingC2×#386×C83C2
socleC23×C83#99
prime radicalC23×D4×C83C22
cosocleC22×D4×C83C23
hypercenterC2×#386D83
hypocenterC83C2×#1390
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C2×#386

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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(21248, 84507);