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C25×Dic7×C53 #49150641

order37100
automorphism?
homologyAbelianization (H1) = C4×C25×C53 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic7×C53
unambiguous semidirect productC7⋊(C4×C25×C53)

Splittings

derived, SylowC7 ⋊ C4×C25×C53
HallC7×C25×C53 ⋊ C4
HallC7×C53 ⋊ C4×C25
HallC7×C25 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C25×C53D7
commutator, hypocenterC7C4×C25×C53
FrattiniC2×C5C5×D7×C53
FittingC2×C7×C25×C53C2
socle, prime radicalC2×C5×C7×C53C2×C5
cosocleC2×C5×C7C2×C5×C53
LCSG ▷ C7
UCSC1 ◁ C2×C25×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37100

Conjugacy classes & character table

13250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37100, 3);