Finite Group Databasebeta

← Prev (#44545640) Next (#44545642) →

C5×Dic15×C107 #44545641

order32100
automorphism?
homologyAbelianization (H1) = C4×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic15×C107
unambiguous semidirect productC3⋊(C5×Dic5×C107)

Splittings

derivedC3×C5 ⋊ C4×C5×C107
HallC3×C52×C107 ⋊ C4
HallC52×C107 ⋊ Dic3
HallC3×C107 ⋊ C5×Dic5
HallC3×C52 ⋊ C4×C107
SylowC52 ⋊ Dic3×C107
SylowC3 ⋊ C5×Dic5×C107

Subgroups

subgroupG/H
center, hypercenterC2×C5×C107D15
commutator, hypocenterC3×C5C4×C5×C107
FrattiniC2C5×D15×C107
Fitting, socle, prime radicalC2×C3×C52×C107C2
cosocleC2×C3×C5C2×C5×C107
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C107

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6420

Conjugacy classes & character table

9630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 39);