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C5×C3⋊(C7⋊Dic35) #28413208

order14700
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C3⋊(C7⋊Dic35)
unambiguous semidirect productC3⋊(C5×C7⋊Dic35)
unambiguous semidirect productC7⋊(C5×Dic105)

Splittings

derivedC3×C5×C72 ⋊ C4×C5
HallC3×C52×C72 ⋊ C4
HallC52×C72 ⋊ Dic3
HallC3×C72 ⋊ C5×Dic5
HallC3×C52 ⋊ C7⋊Dic7
SylowC72 ⋊ C5×Dic15
SylowC52 ⋊ C3⋊(C7⋊Dic7)
SylowC3 ⋊ C5×C7⋊Dic35

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(C5⋊(C7⋊D7))
commutator, hypocenterC3×C5×C72C4×C5
FrattiniC2C5×C3⋊(C5⋊(C7⋊D7))
Fitting, socle, prime radicalC2×C3×C52×C72C2
cosocleC2×C3×C5×C72C2×C5
LCSG ▷ C3×C5×C72
UCSC1 ◁ C2×C5

320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 387);