Finite Group Databasebeta

← Prev (#49185377) Next (#49185379) →

C5×Dic15×C127 #49185378

order38100
automorphism?
homologyAbelianization (H1) = C4×C5×C127 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic15×C127
unambiguous semidirect productC3⋊(C5×Dic5×C127)

Splittings

derivedC3×C5 ⋊ C4×C5×C127
HallC3×C52×C127 ⋊ C4
HallC52×C127 ⋊ Dic3
HallC3×C127 ⋊ C5×Dic5
HallC3×C52 ⋊ C4×C127
SylowC52 ⋊ Dic3×C127
SylowC3 ⋊ C5×Dic5×C127

Subgroups

subgroupG/H
center, hypercenterC2×C5×C127D15
commutator, hypocenterC3×C5C4×C5×C127
FrattiniC2C5×D15×C127
Fitting, socle, prime radicalC2×C3×C52×C127C2
cosocleC2×C3×C5C2×C5×C127
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C127

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7620

Conjugacy classes & character table

11430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38100, 61);