Finite Group Databasebeta

C2×#24906721 #35380239

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24906721

Splittings

SylowC83 ⋊ C2×#1650

Subgroups

subgroupG/H
centerC23#14581762
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×D4⋊C8×C83C2
socleC23×C83#120
prime radicalC22×D4×C83D4
hypercenterC2×D4⋊C8D83
hypocenterC83C2×#1650
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

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, 145403);