Finite Group Databasebeta

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C3×C5×C7⋊Dic35 #28413199

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C7⋊Dic35

Splittings

derivedC5×C72 ⋊ C3×C4×C5
HallC3×C52×C72 ⋊ C4
HallC52×C72 ⋊ C3×C4
HallC3×C72 ⋊ C5×Dic5
HallC3×C52 ⋊ C7⋊Dic7
SylowC72 ⋊ C3×C5×Dic5
SylowC52 ⋊ C3×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C5⋊(C7⋊D7)
commutator, hypocenterC5×C72C3×C4×C5
FrattiniC2C3×C5×C5⋊(C7⋊D7)
Fitting, socle, prime radicalC2×C3×C52×C72C2
cosocleC2×C5×C72C2×C3×C5
LCSG ▷ C5×C72
UCSC1 ◁ C2×C3×C5

320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 378);