Finite Group Databasebeta

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C2×C3×C5⋊D245 #28413013

order14700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C5⋊D245
unambiguous semidirect product(C2×C5)⋊(C3×D245)

Splittings

FittingC2×C3×C52×C49 ⋊ C2
derived, HallC52×C49 ⋊ C22×C3
HallC3×C52×C49 ⋊ C22
HallC3×C49 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D49
SylowC49 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D49

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊D245
commutator, cosocle, hypocenterC52×C49C22×C3
FrattiniC7C2×C3×C5⋊D35
FittingC2×C3×C52×C49C2
socleC2×C3×C52×C7D7
LCSG ▷ C52×C49
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 192);