Finite Group Databasebeta

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C3×C23×Dic55 #29503223

order15180
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic55
unambiguous semidirect productC11⋊(C3×Dic5×C23)

Splittings

derived, HallC5×C11 ⋊ C3×C4×C23
HallC3×C5×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ C3×C4
HallC3×C11×C23 ⋊ Dic5
HallC3×C5×C23 ⋊ Dic11
HallC11×C23 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ C4×C23
HallC5×C23 ⋊ C3×Dic11
HallC3×C11 ⋊ Dic5×C23
HallC3×C5 ⋊ C23×Dic11
SylowC11 ⋊ C3×Dic5×C23
SylowC5 ⋊ C3×C23×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D55
commutator, hypocenterC5×C11C3×C4×C23
FrattiniC2C3×C23×D55
Fitting, socle, prime radicalC2×C3×C5×C11×C23C2
cosocleC2×C5×C11C2×C3×C23
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15180

Conjugacy classes & character table

4002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 9);