Finite Group Databasebeta

C2×#24921266 #36312308

order21248
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#24921266

Splittings

SylowC83 ⋊ C2×#3501

Subgroups

subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC22×C4×D4×C83C2
socleC23×C83C25
prime radicalC23×D4×C83C22
hypercenterC22×C4×D4D83
hypocenterC83C2×#3501
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4×D4

7738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1077472);