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C23×Q8×C293 #34035842

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C25×C293 · Schur multiplier (H2) = C29

Aliases

direct productC23×Q8×C293

Subgroups

subgroupG/H
center, socle, prime radicalC24×C293C22
commutator, Frattini, cosocleC2C25×C293
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C24×C293 ◁ G

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

11720 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49157056, #49158709, #49158720, …
maximal subgroup of#1446×C293, #1784×C293, #1787×C293, …
maximal normal subgroup of#1446×C293, #1784×C293, #1787×C293, …
maximal quotient ofC23×C4⋊C4×C293, C22×C4×Q8×C293, C22×C22⋊Q8×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 262);