Finite Group Databasebeta

C2×#26045880 #37560499

order23872
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26045880

Splittings

SylowC373 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#13093637
commutatorC2×C373C23×C4
FrattiniC2C23×#13093637
FittingC2×Q8×C373C4
socleC22×C373C22×C4
prime radicalC2×#20238611C2
cosocleDic373C24
hypercenterC2×Q8#13093637
hypocenterC373C2×#131
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1626);