Finite Group Databasebeta

C4×#16837143 #28479608

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16837143

Splittings

SylowC59 ⋊ C4×#330

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC4×#97×C59C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenterC4×#97D59
hypocenterC59C4×#330
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60487);