Finite Group Databasebeta

C2×#24909432 #35558333

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24909432

Splittings

FittingC2×#473×C83 ⋊ C2
SylowC83 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#19127834
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC2×#473×C83C2
socleC22×C83#447
prime radicalC2×#19128506C2
hypercenterC2×#473D83
hypocenterC83C2×#2194
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 323497);