Finite Group Databasebeta

← Prev (#44545603) Next (#44545605) →

C3×C25×Dic107 #44545604

order32100
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic107
unambiguous semidirect productC107⋊(C3×C4×C25)

Splittings

derived, SylowC107 ⋊ C3×C4×C25
HallC3×C25×C107 ⋊ C4
HallC25×C107 ⋊ C3×C4
HallC3×C107 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D107
commutator, hypocenterC107C3×C4×C25
FrattiniC2×C5C3×C5×D107
FittingC2×C3×C25×C107C2
socle, prime radicalC2×C3×C5×C107C2×C5
cosocleC2×C5×C107C2×C3×C5
LCSG ▷ C107
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32100

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 2);