Finite Group Databasebeta

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C3×C4×#14579003 #44475841

order30300
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×#14579003

Splittings

derived, SylowC101 ⋊ C3×C4×C25
HallC3×C4×C101 ⋊ C25
HallC4×C101 ⋊ C3×C25
HallC3×C101 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C101⋊C5
commutator, hypocenterC101C3×C4×C25
FrattiniC2×C5C2×C3×C101⋊C5
FittingC3×C4×C5×C101C5
socle, prime radicalC2×C3×C5×C101C2×C5
cosocleC2×C5×C101C2×C3×C5
LCSG ▷ C101
UCSC1 ◁ C3×C4×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30300

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30300, 2);