Finite Group Databasebeta

C2×#21424014 #28587816

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21424014

Splittings

SylowC59 ⋊ C2×#1782

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
Fitting, prime radicalC23×#41×C59C2
socleC23×C59C2×C22⋊C4
cosocleC24×C59C24
hypercenterC23×#41D59
hypocenterC59C2×#1782
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×#41

4062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 168695);