Finite Group Databasebeta

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C4×C25×#3861 #28412911

order14700
isoclinismisoclinic class of #3861
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C25×#3861

Splittings

Fitting, HallC4×C72×C25 ⋊ C3
derived, SylowC72 ⋊ C3×C4×C25
HallC72×C25 ⋊ C3×C4
HallC4×C72 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC4×C25#3861
commutator, hypocenterC72C3×C4×C25
FrattiniC2×C5C2×C5×#3861
FittingC4×C72×C25C3
socle, cosocleC2×C5×C72C2×C3×C5
prime radicalC2×C5×#3861C2×C5
LCSG ▷ C72
UCSC1 ◁ C4×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 90);